A Distribution-Free Theory of Nonparametric Regression

By László Györfi, Michael Kohler, Adam Krzyzak, Harro Walk. 2002

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In Statistics and Probability

Citations in the corpus

Analysis of a Random Forests Model (2010, methodology): “Observe ﬁrst that, by Jensen’s inequality, A slight adaptation of Theorem 4.2 in Gy¨orﬁ et al. [26] shows that ¯ r n is consistent if both diam( A n ( X , Θ)) → 0 in probability and N n ( X , Θ) → ∞ in probability.”
Consistency of Causal Inference under the Additive Noise Model (2013, background): “…possible that the Bayes best fits f(x) = E [Y |x] is smooth while g(y) = E [X|y] is not even continuous; yet it is well known that without smoothness or similar structural conditions, ar- bitrarily bad rates of convergence are possible in regression (see e.g. (Gyorfi et al., 2002), Theorem 3.1).”
Convex-constrained Sparse Additive Modeling and Its Extensions (2017, background): “Asymptotic consistency for certain estimators (such as least-squares) is well-known, although the rate of convergence can be arbitrarily slow (Györfi et al., 2002).”
Metalearners for estimating heterogeneous treatment effects using machine learning (2017, background): “[20] Györfi L, Kohler M, Krzyzak A, Walk H (2006) A distribution-free theory of nonparametric regression.”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, methodology): “Many popular nonparametric regression methods have been shown to be weakly universally consistent, see e.g., (Györfi et al., 2002).”
Fast Distribution To Real Regression (2013, methodology): “Then, Theorem 11.3 of [2] states that the estimated linear predictor ˆ β ∈ R d has an error to the mean conditional response (when truncated) relative an optimal linear predictor β as follows: Using our notation we have that:”
Distribution-Free Distribution Regression (2013, background): “For comprehensive reviews and references, see Ramsay and Silverman [2005], Ferraty and Vieu [2006].”
k-NN Regression Adapts to Local Intrinsic Dimension (2011, background): “For consistency, it is well known that we need k to grow as a function of the sample size n [10] .”
Optimal Rates for the Regularized Least-Squares Algorithm (2007, methodology): “In Section 2 we briefly recall the main concepts of the regression problem in the context of supervised learning theory, [6], [15], [23]; however, the formalism could be easily rephrased using the language of nonparametric regression as in [17].”
Breaking the Curse of Dimensionality with Convex Neural Networks (2014, neutral): “…hidden units grow unbounded and using classical non-Euclidean regularization tools on the output weights, they lead to a convex optimization problem and we provide a detailed theoretical analysis of their generalization performance, with a study of both the approximation and the estimation errors.”
Local Rademacher complexities (2005, methodology): “edures. To analyze the case of unbounded targets, one usually truncates the values at a certain threshold and boundsthe probability of exceeding that threshold (see, e.g., the techniques developed in [12]). The training sample is a sequence (X 1,Y 1),...,(Xn,Yn) of nindependent and identically distr”
Divide and conquer kernel ridge regression: a distributed algorithm with minimax optimal rates (2013, background): “The problem of non-parametric regression is a classical one, and a researchers have studied a wide range of estimators (see, for example, the books of Gyorﬁ et al. (2002), Wasserman (2006), or van de Geer (2000)).”
Batch Policy Learning under Constraints (2019, methodology): “We use the following lemma: Lemma E.5 ((Györfi et al., 2006), theorem 11.4.”
Consistency of Random Forests (2014, methodology): “For partitions that are independent of the Yi’s, consistency can be shown by relatively simple means via Stone’s (1977) theorem for local averaging estimates (see also Györfi et al., 2002, Chapter 6). However, our partitions and trees depend upon the Y -values in the data. This makes things complica”
Just Interpolate: Kernel "Ridgeless" Regression Can Generalize (2018, background): “We refer the readers to [18] for more details.”